One of the key challenges in developing quantum networks is to generate single photons with high brightness, purity, and long temporal coherence. Semiconductor quantum dots potentially satisfy these requirements; however, due to imperfections in the surrounding material, the coherence generally degrades with increasing excitation power yielding a broader emission spectrum. Here we overcome this power-broadening regime and demonstrate an enhanced coherence at exciton saturation where the detected count rates are highest. We detect single-photon count rates of 460 000 counts per second under pulsed laser excitation while maintaining a single-photon purity greater than 99%. Importantly, the enhanced coherence is attained with quantum dots in ultraclean wurtzite InP nanowires, where the surrounding charge traps are filled by exciting above the wurtzite InP nanowire band gap. By raising the excitation intensity, the number of possible charge configurations in the quantum dot environment is reduced, resulting in a narrower emission spectrum. Via Monte Carlo simulations we explain the observed narrowing of the emission spectrum with increasing power. Cooling down the sample to 300 mK, we further enhance the single-photon coherence twofold as compared to operation at 4.5 K, resulting in a homogeneous coherence time, T2, of 1.2 ns, and two-photon interference visibility as high as 83% under strong temporal postselection (∼5% without temporal postselection).